Machin-like formulae
M000006608
$$\pi=8\arctan\left(\frac{1}{3}\right)-8\arctan\left(\frac{1}{4}\right)+8\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{12}\right)+4\arctan\left(\frac{1}{17}\right)+8\arctan\left(\frac{1}{21}\right)$$
Compact formula
8[3] - 8[4] + 8[5] + 4[12] + 4[17] + 8[21]
Lehmer's measure
7.68318